Power factor correction: how to size a capacitor bank and clear a utility penalty

A site running at 0.78 power factor is paying for reactive current it never turns into work, and three different North-American tariff mechanisms will bill it three different ways. Sizing the fix is one equation — Qc = kW × (tan φ1 − tan φ2) — and for an 800 kW load moving from 0.78 to 0.95 it returns 378.9 kVAR, which rounds to a 400 kVAR bank and lands the site at 0.957. That single number then propagates: it sets the capacitor current, the conductor ampacity under NEC 460.8(A), the parallel resonant frequency of the bus at 485 Hz, and the billing determinant Hydro One applies, from 923.1 kVA down to 800 kW. The kW-to-kVA conversion underneath all of it is the same one the transformer sizing calculator runs when a load is entered in kW with a power factor, because power factor is what decides how much apparent power the transformer, the service and the meter have to carry.

Why does a low power factor cost money?

Real work is measured in kilowatts. Inductive equipment — lightly loaded induction motors, welding sets, the magnetizing current of every transformer on site — also draws reactive power in kilovolt-amperes reactive (kVAR) that does no work but still occupies conductors, transformers and switchgear. The vector sum is apparent power in kVA, and power factor is the ratio of the two.

PF = kW ÷ kVA

Utilities recover the cost of carrying that reactive current in one of three ways, and which one applies changes the entire economics of the fix.

BC Hydro’s is the bluntest. Section 7.2.1 of the Electric Tariff requires each customer to “maintain an average Power Factor between 90% lagging and 100% (unity)”. Section 7.2.2 is conditional, not automatic: where a customer neglects or refuses to correct after notice, BC Hydro may, in its sole discretion, apply the surcharge below, suspend it to allow time to comply, or disconnect the premises. Low power factor alone does not trigger it — failure to remediate after notice does. Note the last line of the tariff clause: no surcharge or credit applies to a leading power factor, so over-correction buys nothing and still falls outside the range 7.2.1 specifies.

Hydro One reaches the same place by arithmetic instead of a schedule: billing determinants for demand customers’ distribution charges are set “at the greater of 100 per cent of kW and 90 per cent of kVA where kVA metering is installed.” Ninety per cent is not arbitrary. At exactly 0.90 power factor, 0.9 × (kW ÷ 0.90) = kW, so the two determinants are equal and the clause is dormant. Every point below 0.90 makes the kVA term win.

Billing demand = max(kW, 0.9 × kVA)

Because the utility measures at the revenue meter, correction only has to sit upstream of the CT metering and distribution cabinet to change the bill — its physical position anywhere on the load side of that point is an engineering choice, not a billing one.

How much kVAR does the site need?

Power factor correction supplies the reactive component locally so it circulates between the capacitors and the motors instead of travelling back to the substation. The size of that local supply is the difference between the reactive power drawn now and the reactive power allowed at the target.

Qc = kW × (tan φ1 − tan φ2), where φ = arccos(PF)

The multiplier in brackets is a pure function of the two power factors, so it can be tabulated once and reused. Multiply the table value by the site’s kW.

The kW used must be the billed kW — the demand the tariff clause acts on — not connected load and not nameplate. Utility interval data gives it directly.

Correction pays best where the reactive load is large and steady: plants with banks of induction motors, pumping and compression stations, drive-heavy manufacturing lines. It pays least where loads are small, largely resistive, or already corrected at the equipment.

A worked example: 800 kW at 0.78 power factor, 480 V

A plant is served at 480 V from a 1500 kVA transformer with 5.75 % impedance. Interval data shows 800 kW average billed demand at 0.78 lagging power factor. Target is 0.95.

1. Reactive multiplier now. φ1 = arccos(0.78) = 38.74°, so tan φ1 = 0.8023. The load draws 800 × 0.8023 = 641.8 kVAR.
2. Reactive multiplier at target. φ2 = arccos(0.95) = 18.19°, so tan φ2 = 0.3287. At target the load may draw 800 × 0.3287 = 263.0 kVAR.
3. Correction required. Qc = 800 × (0.8023 − 0.3287) = 800 × 0.4736 = 378.9 kVAR.
4. Bank selected. Round up, not down: 400 kVAR in 8 steps of 50 kVAR. PG&E’s application guidance recommends keeping individual steps at or below 100 kVAR on 480 V installations, because larger steps produce switching transients that stress motor insulation.
5. Resulting power factor. Q2 = 641.8 − 400 = 241.8 kVAR; S2 = √(800² + 241.8²) = 835.7 kVA; PF = 800 ÷ 835.7 = 0.957.
6. Capacitor current. Ic = 400 000 ÷ (√3 × 480) = 481.1 A, which is what the switching contactors, fuses and cable are sized on.
7. Conductor ampacity. NEC 460.8(A) requires at least 135 % of rated capacitor current: 1.35 × 481.1 = 649.5 A.

A smaller Canadian case runs the same way. A 250 kW shop at 600 V and 0.85 power factor needs 250 × (0.6197 − 0.3287) = 72.8 kVAR to reach 0.95, so a 75 kVAR bank in 3 steps of 25 kVAR is specified. It draws 75 000 ÷ (√3 × 600) = 72.2 A and lands at 0.9525 power factor — clear of the 0.90 mark both Canadian tariffs turn on.

What does the correction do to the bill?

The Ontario arithmetic: 923.1 − 800 = 123.1, a 13.3 % reduction in the distribution billing determinant, achieved without removing a single kilowatt of load. The BC arithmetic scales with the whole bill — on a month whose rate-section charges are assumed at $40 000, an illustrative figure that comes from a site’s own invoice and never from the tariff, the 16 % surcharge is 0.16 × 40 000 = $6 400, and it goes to zero. The California arithmetic is a two-sided swing: (85 − 78) × 0.06 = 0.42 % penalty before, and (95.7 − 85) × 0.06 = 0.64 % credit after, so 1.06 % of the charge the adjustment applies to changes sign.

Note what does not change: 800 kW. Capacitors remove kVAR, so a tariff that bills a pure kW demand charge will not move at all. That is a different problem, and behind-the-meter battery storage is the tool for it — see demand charge and peak shaving.

Will the bank resonate with the site’s harmonics?

This is the step that turns a purchase into an engineering problem. The capacitor bank sits in parallel with the source inductance, and every parallel LC pair has a frequency at which it presents a high impedance to injected harmonic current. Setting hX_L1 = X_C1/h and solving gives the order directly from two numbers already known — the short-circuit capacity of the bus and the size of the bank.

h_r = √(S_sc ÷ Q_c), and f_r = 60 × h_r on a 60 Hz system

For the worked example, the infinite-source short-circuit capacity behind the 1500 kVA, 5.75 % transformer is 1500 ÷ 0.0575 = 26 087 kVA, or 26.1 MVA. The bank is switched in steps, so the resonance is not one frequency but a sweep.

Six of the eight step positions sit at or within 5 % of an odd harmonic, and none of the eight is more than 10.3 % away from one. Two of those positions — the 11th at 200 kVAR and the 13th at 150 kVAR — are characteristic six-pulse harmonics that VFDs, rectifiers, EV chargers and UPS front ends produce directly; the 9th and 23rd positions matter only where triplen currents from single-phase electronics or phase unbalance are present. Because IEEE C57.12.00 permits ±7.5 % tolerance on nameplate impedance and h_r varies with √(1 ÷ %Z), the real transformer shifts the whole column by √1.075 = 1.037, close to 4 % — so a design that clears the 11th on paper may not clear it in the field.

The fix is a detuned capacitor bank — a series reactor of p per-unit reactance ahead of each step. Series resonance then sits at a fixed order regardless of how many steps are in:

h_tuned = 1 ÷ √p

A 7 % reactor gives 1 ÷ √0.07 = 3.78, or 3.78 × 60 = 227 Hz, below the 5th harmonic; 5.67 % gives 4.20 (252 Hz) and 14 % gives 2.67 (160 Hz). Note that the 189 Hz commonly printed on 7 % reactor datasheets is the 50 Hz figure — on a North-American 60 Hz system the same reactor tunes to 227 Hz.

The reactor also raises the voltage across the capacitor elements, because the capacitor now carries the full bank voltage plus the reactor drop:

V_C = V_sys ÷ (1 − p)

So a detuned bank on a 480 V bus needs capacitor elements rated above 516 V — the next voltage class, not 480 V units run into their margin. IEEE Std 18 requires capacitors to be designed for operation at or below rated voltage, and capable of continuous operation under contingency system and bank conditions within 110 % of rated rms voltage, 120 % of rated peak voltage including harmonics, 135 % of nominal rms current and 135 % of rated kVAR. Those four numbers are contingency headroom, not a design basis — the IEEE Capacitor Subcommittee added language specifically to stop the 110 % figure being read as a nominal rating.

The distortion ceiling the design has to clear is IEEE 519 Table 1, and the number depends on the bus voltage, which is where most specifications go wrong.

The 2022 edition kept these values and only added “h ≤ 50” to the individual-harmonic heading. The current-side limits, graded by short-circuit ratio, and the measurement rules that go with them are covered in what IEEE 519 requires and how to meet it. Where the harmonic content is severe enough that detuning alone will not hold the bus inside Table 1, the escalation is a tuned passive filter or an active harmonic filter rather than a larger capacitor bank.

What do NEC Article 460 and CEC Section 26 require?

Where Canada differs — starting with how the rules are numbered. The NEC gives each requirement its own clause, which is why a US submittal can cite “460.8(A)” unambiguously. The CEC does not mirror that layout: Rules 26-200 to 26-222 cover conductor sizing, overcurrent protection, disconnecting means, contactor rating, grounding, motor-circuit capacitors and drainage of stored charge as a single block, inside a section that also governs transformers. A Canadian submittal cites the block plus the subject, and reviewers should not expect a Canadian rule number to exist for every NEC subsection. Those rules also exclude capacitors that are components of factory-assembled certified equipment, so a bank supplied as certified assembled equipment is evaluated as an assembly while a field-built bank is evaluated rule by rule.

The difference that costs money is not in the code at all: BC Hydro states a 0.90 requirement outright and Hydro One’s determinant becomes binding below 0.90, where the California utility applies a graded 0.85 reference with a credit above it. The two Canadian tariffs give a site a pass/fail target; the California one gives it a slope.

One clause bridges both codes and is easy to miss: where a capacitor is connected on the load side of a motor’s overload device, NEC 460.9 requires the overload to be set on the improved-power-factor current, not the uncorrected nameplate current. Correcting at the motor and leaving the overload alone under-protects the motor.

What to specify

• Target power factor and the tariff clause behind it — 0.95 lagging here, driven by the 0.90 threshold in BC Hydro T&C 7.2.1 or the Hydro One kVA determinant. The number comes from the utility bill, not a rule of thumb.
• Bank kVAR and step size — 400 kVAR in 8 × 50 kVAR steps here, with individual steps at or below 100 kVAR on a 480 V bus following PG&E’s application guidance, and an automatic controller holding the target as load varies.
• Detuning reactance and the resulting capacitor voltage class — 7 % (tuned to order 3.78, 227 Hz at 60 Hz) with capacitor elements rated above V ÷ (1 − p) = 516 V, taken from a harmonic measurement at the point of common coupling, not assumed.
• Capacitor current and conductor ampacity — 481 A rated current and 650 A conductors under NEC 460.8(A), with fuses and contactors rated for capacitor-switching duty.
• Short-circuit capacity of the bus — 26 087 kVA from the transformer kVA and nameplate %Z, used for the resonance sweep and for the equipment short-circuit rating; take %Z from the nameplate, not a catalogue typical.
• Revenue-point metering — power factor reported where the tariff measures it, so correction is verified against the billing determinant rather than a nameplate assumption.
• Standards basis — capacitors to IEEE Std 18 and UL 810, harmonic performance to IEEE 519, installation to NEC Article 460 or CEC Section 26; state the certification the authority having jurisdiction will require for the assembly.

Common mistakes

• Rounding the bank down. 378.9 kVAR rounded to 350 kVAR yields 0.9394, not 0.95; 300 kVAR yields 0.9196 and leaves only 0.02 of margin before the next load addition drops the site back into a penalty band. Recompute with PF = P ÷ √(P² + (Q1 − Qb)²) before signing off.
• Sizing on connected load instead of billed demand. The tariff clause acts on metered kW over the billing period. Connected kW oversizes the bank and pushes power factor leading at light load — outside the 90 % lagging to unity range BC Hydro T&C 7.2.1 specifies, and earning no credit under the tariff. Interval data and step-down logic catch this.
• Reading the harmonic limit off the wrong row. IEEE 519 Table 1 is graded by the voltage at the point of common coupling, and the ≤1 kV row is the looser one. Specifying the 1 kV to 69 kV row at a 480 V PCC fails a bank that actually complies; quoting the ≤1 kV row at an MV PCC passes one that does not. Match the row to the PCC voltage before writing the acceptance criterion.
• Checking resonance only at full bank output. h_r at 400 kVAR says nothing about h_r at 200 kVAR, and the intermediate steps are where a stepped bank usually lands on a characteristic harmonic. Run h_r = √(S_sc ÷ Q_c) for every step position, not just the full bank, then detune.
• Leaving a motor overload set on uncorrected current. NEC 460.9 requires the overload device to be set on the improved-power-factor current when the capacitor is on the load side of that device. A 481 A correction at the bus does not touch this, but capacitors installed at individual motors do.

Where Entogo fits

Entogo’s automatic power-factor-correction capacitor bank is a 480 V stepped design with detuned reactors, built alongside low-voltage switchgear and MCCs, metering cabinets and transformers in one vertically integrated factory in Toronto. It is designed and built to IEEE Std 18, UL 810 and NEMA CP-1, specified against IEEE 519 at the point of common coupling, and installed to NEC Article 460 or CEC Section 26; UL (cULus)/CSA certifiable on request.

Where the correction, the metering and the upstream distribution equipment are specified together, the resonance check and the transformer %Z that drives it are settled before release to manufacturing rather than discovered at commissioning. For a site-specific review, run the load through the transformer sizing calculator and bring the interval data to the industrial and EPC or substations and power distribution team; sites also sizing service capacity from scratch should start with how to size a transformer or a transformer and distribution quote, because the kW-to-kVA step is the same one.

The decision this article does not make for a site is whether to correct at all. A bank earns its capital only where a tariff actually prices reactive power and the harmonic spectrum has been measured rather than assumed. Establish those two things first — the kVAR arithmetic above is the easy part, and it is the part a bank sized from a rule of thumb can still get right by accident while failing everything else.